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The GW method, which can describe accurately electronic excitations, is one of the most widely used ab initio electronic structure technique and allows the physics of both molecular and condensed phase materials to be studied. However, the applications of the GW method to large systems require supercomputers and highly parallelized software to overcome the high computational complexity of the method scaling as O(N 4 ). Here, we develop efficient massivelyparallel GW software for the plane-wave basis set by revisiting the standard GW formulae in order to discern the optimal approaches for each phase of the GW calculation for massively parallel computation. These best numerical practices are implemented into the OpenAtom software which is written on top of Charm++ parallel framework. We then evaluate the performance of our new software using range of system sizes. Our GW software shows significantly improved parallel scaling compared to publically available GW software on the Mira and Blue Waters supercomputers, two of largest most powerful platforms in the world.

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Formulations of graph algorithms using sparse linear algebra have yielded highly scalable distributed algorithms for problems such as connectivity and shortest path computation. We develop the first formulation of the Awerbuch-Shiloach parallel minimum spanning forest (MSF) algorithm using linear algebra primitives. We introduce a multilinear kernel that operates on an adjacency matrix and two vectors. This kernel updates graph vertices by simultaneously using information from both adjacent edges and vertices. In addition, we explore optimizations to accelerate the shortcutting step in the Awerbuch-Shiloach algorithm. We implement this MSF algorithm with Cyclops, a distributed-memory library for generalized sparse tensor algebra. We analyze the parallel scalability of our implementation on the Stampede2 supercomputer.